EASTON — The three candidates ­vying for the Republican nomination in the US Senate special election faced off in their first debate Tuesday night in a lively exchange before a crowd of about 300 that showcased the candidates’ ­divergent profiles.

Michael J. Sullivan — who previously served as US attorney and director of the US Bureau of Alcohol, Tobacco, Firearms, and Explosives — played relaxed senior statesman, unruffled by any questions tossed his way. He shrugged off a Globe story about his campaign manager repurposing policy statements used last election cycle for the website of congressional candidate Richard R. Tisei.

“There’s nothing on there that I would say that contradicts positions that I’ve taken publicly,” Sullivan said at the forum at Stonehill College. “It’s hard for me to be critical of the people who are volunteering and trying to be helpful.”

State Representative Daniel B. Winslow of Norfolk, who
served in the Romney admin­istration and as a judge, portrayed himself as an outsider who would shake up the status quo.

“If you think things are going well, vote for the other guys, because I’m here to try to change things in Washington,” he said, panning sequestration as an example of the problems and deriding Democrats for “scare tactics.”

Gabriel E. Gomez, a 47-year-old private equity investor from Cohasset, was the halting newcomer leaning heavily on his life story as the son of Colombian immigrants and his years as a US Navy SEAL.

“We cannot send another ­career politician down to D.C.,” Gomez said, repeating the ­descriptor he used at least a half-dozen times in the debate.

All three committed to serve no more than two terms if elected, though Winslow, 54, and Sullivan, 58, said it would be difficult to impose a term limit on members of Congress.

None of the three candidates supported an assault weapons ban to contain gun violence, though Gomez advocated stricter background checks, particularly for the mentally ill.

“People like to think that bans are effective,” Sullivan said. “They’re completely in­effective. I’ve seen it from my experience.”

He also noted that he was at ATF at the time of a mass shooting at Virginia Tech by a gunman who had been ruled mentally ill. He called it “a complete failure in terms of our system.”

“We’ve done a great job preventing prohibited persons who are felons from getting guns,” Sullivan said. “We’ve done a horrible job of preventing people who are mentally ill.”

On immigration, Gomez noted that as the son of immigrants, he favors a pathway to citizenship that would be “not easy, but also not impossible.”

Winslow called for a comprehensive approach to immigration reform, sealing off ­porous borders, speeding up the process for those seeking to immigrate legally, and expediting deportation of those who commit crimes. Neither he nor Gomez called for amnesty for any particular group of illegal immigrants.

Sullivan, on the other hand, said he would give amnesty to undocumented immigrants who had served the United States in the military.

Gomez, asked about his ­effort to persuade Governor ­Deval Patrick to appoint him ­interim senator after John F. Kerry left the seat vacant to ­become secretary of state, said he would release on Wednesday the letter he sent seeking the appointment.

Asked about whether they would work with freshman US Senator Elizabeth Warren on prosecuting banks, Gomez ­said he could work with anyone. “I don’t ­believe that any bank or any insti­tution is too big to fail or too big to prosecute,” he said.

Winslow criticized federal prosecutors for targeting some for justice, and not others, specifically pointing to US Attorney Carmen M. Ortiz’s prosecution of Internet activist Aaron Swartz on federal hacking charges, a case that has been seen by some critics as overly aggressive.

“There has to be some sense of proportion,” said Winslow.

Sullivan criticized President Obama’s Department of Justice, but for different reasons, saying it should have prosecuted Wall Street, beyond seeking financial penalties, but instead focused on individuals and not corporations.

“Do we prosecute a company just for the sake of saying we’re tough and have [innocent] people lose their jobs?” Sullivan said. “Senators should be making the law; the courts should be interpreting it.”

Later, asked whether Ortiz went too far in prosecuting Swartz, who took his own life, Sullivan said there were situations when he led the same ­office when suspects awaiting trial committed suicide.

Winslow said the government should “reexamine our criminal laws and shift some of the discretion away from prosecutorial authorities, perhaps back to the courts.”

Gomez said that “the thing that alarms me is the potential politicization of a department such as US attorney,” and he called it “just another example of why people don’t trust career politicians down in Washington, D.C.”

The event was hosted by ­Peter Ubertaccio, director of the Martin Institute at Stonehill College, and cosponsored by GateHouse MA/WickedLocal, WCVB (Channel 5), and WGBH radio.